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In logic, an **inverse** is a type of conditional sentence which is an immediate inference made from another conditional sentence. More specifically, given a conditional sentence of the form , the inverse refers to the sentence . Since an inverse is the contrapositive of the converse, inverse and converse are logically equivalent to each other.^{[1]}

For example, substituting propositions in natural language for logical variables, the inverse of the following conditional proposition

- "If it's raining, then Sam will meet Jack at the movies."

would be

- "If it's not raining, then Sam will not meet Jack at the movies."

The inverse of the inverse, that is, the inverse of , is , and since the double negation of any statement is equivalent to the original statement in classical logic, the inverse of the inverse is logically equivalent to the original conditional . Thus it is permissible to say that and are inverses of each other. Likewise, and are inverses of each other.

The inverse and the converse of a conditional are logically equivalent to each other, just as the conditional and its contrapositive are logically equivalent to each other.^{[1]} But *the inverse of a conditional cannot be inferred from the conditional itself* (e.g., the conditional might be true while its inverse might be false^{[2]}). For example, the sentence

- "If it's not raining, Sam will not meet Jack at the movies"

cannot be inferred from the sentence

- "If it's raining, Sam will meet Jack at the movies"

because in the case where it's not raining, additional conditions may still prompt Sam and Jack to meet at the movies, such as:

- "If it's not raining and Jack is craving popcorn, Sam will meet Jack at the movies."

In traditional logic, where there are four named types of categorical propositions, only forms A (i.e., "All *S* are *P"*) and E ("All *S* are not *P"*) have an inverse. To find the inverse of these categorical propositions, one must: replace the subject and the predicate of the inverted by their respective contradictories, and change the quantity from universal to particular.^{[3]} That is:

- "All
*S*are*P"*(*A*form) becomes "Some non-*S*are non-*P*". - "All
*S*are not*P"*(*E*form) becomes "Some non-*S*are not non-*P".*

- ^
^{a}^{b}Taylor, Courtney K. "What Are the Converse, Contrapositive, and Inverse?".*ThoughtCo*. Retrieved 2019-11-27.`{{cite web}}`

: CS1 maint: url-status (link) **^**"Mathwords: Inverse of a Conditional".*www.mathwords.com*. Retrieved 2019-11-27.**^**Toohey, John Joseph. An Elementary Handbook of Logic. Schwartz, Kirwin and Fauss, 1918